$k$-connectivity of inhomogeneous random key graphs with unreliable links
This work addresses connectivity robustness in wireless sensor networks, but it is incremental as it generalizes previous theoretical results.
The paper tackles the problem of ensuring secure and reliable connectivity in wireless sensor networks by analyzing a model combining heterogeneous key predistribution and unreliable links, deriving conditions for k-connectivity with high probability and supporting them with numerical results.
We consider secure and reliable connectivity in wireless sensor networks that utilize a heterogeneous random key predistribution scheme. We model the unreliability of wireless links by an on-off channel model that induces an Erdős-Rényi graph, while the heterogeneous scheme induces an inhomogeneous random key graph. The overall network can thus be modeled by the intersection of both graphs. We present conditions (in the form of zero-one laws) on how to scale the parameters of the intersection model so that with high probability i) all of its nodes are connected to at least $k$ other nodes; i.e., the minimum node degree of the graph is no less than $k$ and ii) the graph is $k$-connected, i.e., the graph remains connected even if any $k-1$ nodes leave the network. We also present numerical results to support these conditions in the finite-node regime. Our results are shown to complement and generalize several previous work in the literature.